Question

An Insect Of Negligible Mass Is Sitting On A Block Of Mass M, Tied With A Spring Of Force Constant K. The Block Performs Simple Harmonic Motion With Amplitude A In Front Of A Plane Mirror Placed As Shown. The Maximum Speed Of Insect Relative To Its Image Will Be

Answer 1

Given :

Mass of the block = M

Force constant of spring = k

Amplitude of the block = A

To Find :

The maximum speed of the insect relative to its image = ?

Solution :

• The insect and the block are moving upwards and let us assume that the maximum velocity is v

• Now the velocity of insect in the mirror will be v at a direction of 60° with the vertical direction

          $v_{Insect} = v_{image} = v_{max}$

• The relative velocity is given by

         $v_{rel} = \sqrt{v^{2}+ v^{2}-2 v^{2} Cos120}$

         $v_{rel} = \sqrt{3} v_{max}$

• We know that   $v_{max} = A\omega$        

                                 $v_{max} = A\sqrt{\frac{k}{M} }$

The maximum speed of insect is    $v_{max} = A\sqrt{\frac{k}{M} }$